KR102372569B1 - Systems and methods for implementing electrically tunable metasurfaces - Google Patents

Abstract

Systems and methods according to embodiments of the invention implement electrically tunable metasurfaces. In one embodiment, an electrically tunable metasurface reflectarray comprises a mirrored surface, a conductive layer, a dielectric layer, wherein the conductive layer and the dielectric layer are in direct contact to form a conductor-dielectric interface, and a plurality of subwavelength antennas; an element and a power source configured to establish a potential difference between the at least one subwavelength antenna element and the mirrored surface, wherein the potential difference between the subwavelength antenna element and the mirrored surface corresponds to an electrically tunable metasurface reflectarray By applying an electric field to the region and the applied electric field in association with the geometry and material composition of each of the dielectric layer, the conductive layer, and the subwavelength antenna elements, the electrically tunable metasurface reflectarray produces the propagation characteristics of the incident electromagnetic wave. can be measurably enhanced.

Description

SYSTEMS AND METHODS FOR IMPLEMENTING ELECTRICALLY TUNABLE METASURFACES

Cross-referencing of related applications

This application claims priority based on U.S. Provisional Patent Application No. 61/948,810 filed on March 6, 2014, the entire contents of which are incorporated herein by reference.

Federal funding application

This invention was made with government support under FA9550-12-1-0488 and FA9550-12-1-0024 as determined by the Air Force. The government has certain rights in this invention.

field of invention

The present invention relates generally to the implementation of electrically tunable metasurfaces.

A metamaterial generally refers to an artificial synthetic material characterized by a repeating pattern of structural elements having a characteristic length of a level shorter than the wavelength of a wave. For example, 'photonic metamaterials' (also known as 'optical metamaterials') - which function to control the propagation of visible light - contain structural elements with characteristic lengths on the order of nanometers, whereas Wavelengths are on the order of several hundred nanometers. A lot of research has been conducted on the development of these materials with practical optical properties, although it is against intuition. For example, metamaterials with a negative refractive index have been developed and are the subject of many studies.

A 'metasurface' can be considered a two-dimensional metamaterial as long as it is characterized by a repeating pattern of sub-wavelength structures, and can offer many of the same advantages as a metamaterial. Furthermore, metasurfaces can be advantageous over metamaterials in many cases. For example, metasurfaces can be made to transmit light more efficiently than metamaterials.

Systems and methods according to embodiments of the invention implement electrically tunable metasurfaces. In one embodiment, an electrically tunable metasurface reflectarray comprises a mirrored surface, a conductive layer, a dielectric layer, wherein the conductive layer and the dielectric layer are in direct contact to form a conductor-dielectric interface, and a plurality of subwavelength antennas; an element and a power source configured to establish a potential difference between the at least one subwavelength antenna element and the mirrored surface, wherein the potential difference between the subwavelength antenna element and the mirrored surface corresponds to an electrically tunable metasurface reflectarray By applying an electric field to the region and the applied electric field in association with the geometry and material composition of each of the dielectric layer, the conductive layer, and the subwavelength antenna elements, the electrically tunable metasurface reflectarray produces the propagation characteristics of the incident electromagnetic wave. can be measurably enhanced.

In another embodiment, the electrically tunable metasurface further comprises a second power source configured to establish a second potential difference between the mirrored surface and the at least one other subwavelength antenna element.

In another embodiment, the power source is configured to establish a plurality of potential differences between the plurality of subwavelength antenna elements and the mirrored surface.

In yet another embodiment, an electrically tunable metasurface reflectarray characterized by wavelengths less than 10 μm by an electric field applied in connection with the geometry and material composition of each of the dielectric layer, the conductive layer, and the subwavelength antenna elements. propagation characteristics of an incident electromagnetic wave included within at least a portion of the electromagnetic spectrum may be measurably enhanced.

In yet another embodiment, at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength that is less than or equal to a wavelength approximately corresponding to a wavelength of the near-infrared electromagnetic wave.

In a further embodiment, when a region of an electrically tunable metasurface is exposed to an electric field, an incident reflected electromagnetic wave comprised within at least a portion of the electromagnetic spectrum exhibits a phase shift based on the magnitude of the applied electric field.

In yet another embodiment, at least a portion of the electromagnetic spectrum is characterized by an electromagnetic wave having a wavelength approximately corresponding to a wavelength of a near-infrared electromagnetic wave.

In yet another embodiment, at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength that is less than or equal to a wavelength approximately corresponding to a wavelength of visible light.

In yet another embodiment, at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength approximately corresponding to a wavelength of visible light.

In another embodiment, the conductive layer comprises one of a nitride-based material, silver, copper, gold, aluminum, an alkali metal, an alloy, a transparent conductive alloy, and graphene.

In another embodiment, the conductive layer comprises indium tin oxide.

In another embodiment, the dielectric layer comprises a dielectric oxide.

In another embodiment, the dielectric layer comprises aluminum oxide.

In a further embodiment, the mirrored surface comprises gold and at least one of the plurality of subwavelength antenna elements comprises gold.

In another embodiment, when a region of an electrically tunable metasurface reflectarray is exposed to an electric field, the charge carrier concentration at the conductor-dielectric interface in the region is altered based on the magnitude of the applied electric field, wherein the change a phase shift of the reflected incident electromagnetic wave, which is within at least a portion of the electromagnetic spectrum by

In another embodiment, a change in charge carrier concentration from 1x10 ¹⁹ cm ^-3 to 1x10 ²¹ cm ^-3 is sufficient to shift the phase of an incident reflected electromagnetic wave that is within at least a portion of the electromagnetic spectrum by at least 2π.

In yet another embodiment, at least one of the plurality of sub-wavelength antenna elements conforms to a rod-shaped geometry.

In another embodiment, at least one of the plurality of sub-wavelength antenna elements conforms to a V-shape geometry.

In yet another embodiment, at least one of the plurality of sub-wavelength antenna elements conforms to a split ring geometry.

In yet another embodiment, at least two of the plurality of sub-wavelength antenna elements are coupled to a same conducting element coupled to the power source.

In another embodiment, rows of sub-wavelength antenna elements are connected to respective conductive elements that are connected to a power source.

1A-1B show a prior art metasurface.
2a-2b show a metasurface reflectarray and its reflection angle as a function of the angle of incidence.
3A-3B illustrate an electrically tunable metasurface reflectarray comprising rod-shaped subwavelength antenna elements, in accordance with certain embodiments of the invention.
4 illustrates a prospective material that may be embodied in a metasurface in accordance with certain embodiments of the invention.
5a-5c show an electrically tunable metasurface comprising an array of gold subwavelength antenna elements, an ITO-Al ₂ O ₃ interface, and a gold mirror, in which case the rows of subwavelength antenna elements are of the invention; It remains at the same potential according to some embodiments.
6 illustrates a sub-gated electrically tunable metasurface in accordance with certain embodiments of the invention.
7A-7C show data showing a resonant split with application of a potential difference, which may be used in accordance with certain embodiments of the invention.
8A-8B illustrate how reflection and phase shift vary as a function of charge carrier concentration and wavelength in accordance with certain embodiments of the invention.
9A-9B illustrate how reflection and phase shift vary as a function of charge carrier concentration in accordance with certain embodiments of the invention.

Referring now to the drawings, a system and method for implementing an electrically tunable metasurface is illustrated. In many embodiments, the electrically tunable metasurface comprises the phase and/or amplitude of reflected and/or transmitted electromagnetic waves, including, but not limited to, electromagnetic waves having wavelengths on the order of visible and/or near-infrared (near-IR) light. and an array of subwavelength antenna elements having a complex dielectric function that is electro-optically tunable to control In many embodiments, such metasurfaces are used to implement optical beamformers.

Metamaterials and metasurfaces are considered to have various potentials for robust control of electromagnetic waves. However, much of the progress in this field has been limited to metasurfaces, which are largely fixed in the electromagnetic response they generate, and configured to operate at limited bandwidths. Consequently, there is a lot of interest in developing “tunable” metamaterials/metasurfaces that allow for dynamic post-fabrication control of the generated electromagnetic response. In particular, interest is focused on the potential for developing tunable metamaterials/metasurfaces configured to manipulate electromagnetic waves with wavelengths corresponding to those of near-infrared and visible light. In general, it would be useful to be able to control reflected and refracted waves originating from electromagnetic waves having wavelengths at or below the wavelength of near-infrared waves. Thus, see, for example, “Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability,” to Pryce et al. ( Nano Lett . 2010, 10. 4222-4227, DOI:10.1021/nl102684) uses a mechanical high-strain of an elastomeric substrate to controllably modify the distance between the resonant elements, at optical frequencies larger than the resonant linewidth of approximately 400 nm. A compliant metamaterial with wavelength tunability is disclosed. Since the disclosure of "Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability" relates, inter alia, to modifying metamaterials to tune electromagnetic response properties, their entirety is encompassed by the present invention.

Notwithstanding this, in many practical applications it may not be desirable to have to rely on mechanical strain to realize the desired electromagnetic response characteristics. Moreover, in many instances, it may be desirable to allow for even more subtle control of the electromagnetic response of the metasurface. For example, in many instances it may be desirable to be able to locally control the electromagnetic response properties within the metasurface. Additionally, it is worth mentioning that many of the metasurfaces that have been developed so far configured to work for visible light are optically inefficient. For example, many existing optical metasurfaces have optical efficiencies of less than 10%. As can be seen, it may be desirable to implement metasurfaces with improved optical efficiency. While much of the discussion that follows describes metamaterials used for light reflection to realize improved optical efficiencies, it should be understood that similar techniques can be used to create refractive metasurfaces with dynamically tunable refractive indices. .

Thus, in many embodiments of the invention, a tunable metasurface configured to respond to electromagnetic waves having a wavelength of less than 10 μm, including, for example, near infrared and visible light, is implemented, in which case using a localized electric field, the metasurface is implemented. It is possible to manipulate the localized electromagnetic response characteristics of Additionally, many embodiments of the invention implement metasurfaces with improved optical efficiency. As you can see, such a rigid metasurface can be implemented in practice in various applications. For example, in many embodiments, an optical beamforming metasurface is implemented. In many embodiments, it is possible to realize holography using the described robust metasurface. In various embodiments, the described robust metasurface can be used to realize animated holography. In many embodiments, it is possible to realize cloaking devices using the described rigid metasurface. Moreover, the described robust metasurface can be implemented in a variety of applications that may benefit from this robust wavefront forming function. Before giving a detailed description of the structure of metasurfaces, an overview of the physics underlying metasurface phenomena is now presented below.

commonly known metasurface Physics

Before discussing the subject of this application, tunable metasurfaces, it is useful to review some of the generally known physics governing metasurface phenomena. When discussing metamaterial/metasurface phenomena, a generalized version of Snell's law can often be used to model the electromagnetic response. A generalized version of Snell's law for refraction can be expressed as:

here,

n _i is the refractive index of the first medium through which the incident light passes,

n _t is the refractive index of the second medium through which the incident light passes,

θ _i is the angle of incidence of the incident light,

θ _t is the angle of refraction of the light refracted when the light passes through the second medium,

dφ / dx characterizes the phase change of the light wave in the plane of incidence,

λ ₀ is the wavelength of the incident light.

Similarly, a generalized version of Snell's law for reflection can be expressed as:

The same convention as before was used, and θ _r is the reflection angle of the reflected light. In many circles, the values ( dφ / dx ) are considered wave-vectors. It can also be noted that much characterizes a generalized version of Snell's law as an example of conservation of momentum.

For a discussion of a generalized version of Snell's law see "Light Propagation with Phase Discontinuities; Generalized Laws of Reflection and Refraction," to Yu et al. ( Science . 2011 Oct 21;334 (6054): 333-7. doi: 10.1126/science.1210713.). Since the disclosure of "Light Propagation with Phase Discontinuities; Generalized Laws of Reflection and Refraction" relates, inter alia, to a generalized version of Snell's law, its entirety is incorporated herein by reference. Refraction and reflection that originate because of a phase change in the plane of incidence may be referred to as 'anomalous refraction' and 'anomalous reflection', respectively.

In any case, it can be seen from a generalized version of Snell's law that the angle of refraction and reflection from the incident light source is a function of the phase change in the plane of incidence. The operation of metasurfaces generally depends on this phenomenon. In general, metasurfaces use a resonator - often in the form of subwavelength elements - to cause a phase change (usually abrupt) of the incident light. Such resonators can also be used to change the amplitude and polarization of incident light. In general, the phase shift (and amplitude and polarization response) caused by sub-wavelength antenna elements is a function of the geometry of the antenna. Thus, so far, metasurfaces have implemented various types of antenna elements, including, but not limited to, v-shaped antenna elements, rods, and split ring resonators. As previously suggested, antenna elements typically have dimensions that are much shorter than the wavelength of the electromagnetic wave they encounter.

Metasurfaces often realize their intrinsic properties due to surface plasmon phenomena. In general, surface plasmons, which are charge oscillations of free electrons near the metal surface, arise from interactions with light and matter, and typically arise at the conductor-dielectric interface. Under certain conditions, light combines with surface plasmons to produce self-contained, propagating electromagnetic waves, known as surface plasmon polylithons. Such surface plasmon polariton generation is often related to the intrinsic optical properties that can be realized with metasurfaces. Such metasurfaces may be referred to as plasmonic metasurfaces.

1A and 1B show a prior art metasurface comprising phased array antenna elements that exhibit the ability to shift the phase of an incident infrared electromagnetic wave by a desired degree. In particular, FIG. 1A shows a metasurface 102 comprising a plurality of v-shaped phased array antenna elements 104 . The highlighted v-shaped antenna elements 106 represent the various antenna elements used to show '2π phase coverage'. In other words, each of the illustrated sub-wavelength antenna elements basically has the effect of shifting the phase of the incident infrared electromagnetic wave by a predetermined degree, and the degree of shift depends on the geometry of the antenna element. Accordingly, the illustrated eight sub-wavelength antenna elements 106 have different geometries, and thus shift the incident wave to different magnitudes. In the illustrated example, the different geometries show the ability to shift the phase of the incident wave by a magnitude of 0 to 2π, and this shift is It depends on the geometry of the antenna element. The antenna element has a length of approximately 2 μm, so that the antenna elements are configured to meet an infrared wavelength (eg, λ=8 μm). Importantly, since the geometry of the antenna elements is fixed, the respective phase shifts they cause are also fixed post-fabrication.

1B shows how an incident infrared electromagnetic wave interacts with an antenna array. It should be noted that the propagation direction changes, which is a phenomenon that does not appear well in reality.

The above-described physical phenomenon underlying metasurface operation can also be found in metasurface reflectarrays, and the principle is related to reflected light. Typically, these metasurfaces are bounded by a mirror surface, which effectively 'cancels' the transmitted light. Note that these surfaces can be made to be high-efficiency, to conserve polarization, and to operate at or near optical frequencies. 2a-2b show prior art reflectarray metasurfaces configured to meet wavelengths at optical frequencies. In particular, the metasurface 202 includes constituent antenna elements 204 sized to cause a particular phase shift. A detail view of the sub-cell 206 is also shown, showing that the sub-cell includes antenna elements 208 disposed on a dielectric layer 210 , the dielectric layer 210 itself being on a metal film 212 . is placed on Specifically, the illustrated prior art structure uses antenna elements 208 made of gold, a dielectric layer 210 made from MgF ₂ , and a metal film 212 made from gold. The thickness of the gold antenna is approximately 30 nm, the thickness of the dielectric layer is approximately 50 nm, and the thickness of the gold film is approximately 130 nm. The operating wavelength of the structure shown is approximately 850 nm. FIG. 2A also shows that when the metasurface is illuminated with light 222 having a normal angle of incidence, the reflected light 224 is reflected at an angle - contrary to intuition. This is the metasurface effect.

2B shows a plot of the angle of reflection as a function of angle of incidence. Shaded area 252 marks the area where incident light is reflected back towards itself counter-intuitively. This plot shows that there is a critical angle above which there is no reflection.

Based on the above overview of metasurface physics and behavior, dynamic for propagation of electromagnetic waves of wavelengths of 10 μm or less, including but not limited to optical and/or near-infrared waves, according to embodiments of the invention An opto-electrically tunable metasurface, which provides control, is now discussed below.

approximately 10㎛ An electrically tunable metasurface for controlling the propagation of electromagnetic waves with sub-wavelengths

In many embodiments, an electrically tunable metasurface is provided for controlling the propagation of electromagnetic (“EM”) waves having wavelengths less than approximately 10 μm, including, for example, near-infrared electromagnetic waves and visible electromagnetic waves, in this case the metasurface. An electric field can be applied locally to dynamically enhance the electromagnetic response characteristics of As can be seen from the discussion above, the electromagnetic response of the metasurface is strongly correlated with the geometry of the structure (eg, the geometry of the resonator being implemented). As we also know, the electromagnetic response is also a function of the constituent material of the metasurface. In general, the structure and composition of the metasurface can be tailored to implement a desired electromagnetic response characteristic by selectively implementing a particular structure/composition capable of eliciting the desired electromagnetic response characteristic. Many embodiments of the present invention also exploit the novel understanding that the local carrier concentration in the conductor of a conductor-dielectric complex within a plasmonic metasurface can also affect the electromagnetic response properties of the metasurface. Thus, in many embodiments of the invention, the metasurface comprises a conductor-dielectric interface and an array of subwavelength antenna elements in an arrangement that renders the metasurface responsive to electromagnetic waves of wavelengths less than 10 μm, wherein the application of the electric field is the electromagnetic wave of the metasurface. Reinforces response characteristics. It is judged that the applied electric field changes the carrier concentration at the surface of the conductor-dielectric interface, which in turn alters the electromagnetic response characteristics of the metasurface.

For example, in many embodiments, an electrically tunable metasurface reflectarray is implemented. For example, FIGS. 3A-3B illustrate an electrically tunable metasurface reflectarray, comprising an array of rod-shaped subwavelength antenna elements. In particular, FIG. 3A shows a top view of a metasurface 302 comprising rod-shaped subwavelength antenna elements 304 . 3B shows a cross-sectional portion of a metasurface 302 that includes a subwavelength antenna element 304 . In particular, the electrically tunable metasurface reflectarray features an underlying mirror, on which a conductive layer is disposed and a dielectric layer disposed thereon. In the embodiment shown, the subwavelength antenna element is disposed on the dielectric layer. When an electric field is locally applied to the metasurface, the electromagnetic response properties can change as a result - it is judged that the application of the electric field modifies the charge carrier concentration in the conducting layer at the conductor-dielectric interface, i.e., in the region of the active conducting layer, and , so it is judged to cause a change in the electromagnetic response of the metasurface. In the illustrated embodiment, a potential difference is applied directly between the mirror and the subwavelength antenna element, establishing an electric field. The potential difference may be established in various ways according to an embodiment of the invention. In many embodiments, one or more power sources may be used to build a potential difference between the subwavelength antenna elements and the mirrored surface. In many embodiments, the power source may establish a plurality of potential differences between the respective plurality of subwavelength antenna elements and the mirrored surface. In accordance with an embodiment of the invention, any of a variety of circuits may be used to realize application of a potential difference at an electrically tunable metasurface. While application of a potential difference has been discussed, it is apparent that an electric field can be built up in an electrically tunable metasurface in a variety of ways in accordance with many embodiments of the invention.

Additionally, as will be appreciated, the specific geometry of the subwavelength antenna elements and the thickness of the dielectric and conductive layers may be selected based on the desired electromagnetic response characteristics. Moreover, the specific materials implemented within these layers and sub-wavelength antenna elements may also affect the electromagnetic response properties of the metasurface reflectarray. Thus, as will be appreciated, the material selected for forming the metasurface reflectarray can also be based on a desired electromagnetic response. For example, in some embodiments, the conductive layer comprises one of indium tin oxide, graphene, conductive nitride, and titanium nitride. “Low-Loss Plasmonic metamaterials”, by Boltasseva et al. ( Science 331, 290 (2011); DOI: 10.1126/science. 1198258) discloses considerations in material selection for implementation in metamaterials. "Low-Loss Plasmonic Metamaterials" are incorporated herein in their entirety, particularly since they disclose considerations of the material selection process in metamaterial formation. Figure 4, taken from "Low-Loss Plasmonic Metamaterials", shows several materials that can be used for the implementation of metasurface reflectarrays based on targeted electromagnetic wavelengths. Likewise, any suitable dielectric layer may be implemented. For example, in many embodiments, a dielectric oxide is implemented. In various embodiments, aluminum oxide (Al ₂ O ₃ ) is implemented as the dielectric layer. Any suitable material presented in FIG. 4 may be used to implement a metasurface reflectarray in accordance with an embodiment of the invention. In some embodiments, the materials implemented are materials compatible with existing manufacturing infrastructures. For example, in many embodiments, the conductive layer material is a material that can be readily incorporated into a modern semiconductor fabrication house. In general, as will be appreciated, the metasurface shown in FIGS. 3A-3B may be modified in any of a variety of ways, based on desired behavior and desired electromagnetic response characteristics in accordance with many embodiments of the invention. .

In many embodiments, a plurality of subwavelength antenna elements are brought into contact with a single conducting element, such that they remain at the same potential. In such an arrangement, an electric field can be more easily built - for example, a potential difference can be more easily applied between a plurality of subwavelength antenna elements and a mirror. For example, FIGS. 5A-5C show a metasurface reflectarray comprising rows of subwavelength antenna elements, each connected by a respective single conducting element. In particular, FIG. 5A shows an isometric view of an electrically tunable metasurface reflectarray. More specifically, FIG. 5A shows a metasurface 502 comprising rod-shaped subwavelength antenna elements 504 , which are connected by a conducting element 506 and thus held at the same potential. . Thus, Figure 5a shows that a voltage is applied between the first row of subwavelength antenna elements and the mirrored surface below, and that this voltage can be used to locally modify the electromagnetic response characteristics. In many embodiments, different phases may be applied to adjacent rows of subwavelength antenna elements to perform optical beamsteering. In other embodiments, a voltage may be applied to change the phase at the wavefront of the reflected light in any manner suitable to the requirements of the particular application. FIG. 5B shows a scanning electron microscope (SEM) image of the electrically tunable metasurface reflectarray shown in FIG. 5A.

5C shows a cross-sectional view of a portion of the electrically tunable metasurface reflectarray presented in FIGS. 5A-5B. In particular, the metasurface reflectarray features an underlying gold mirror, on which an ITO layer is disposed, on which an aluminum oxide - Al ₂ O ₃ - dielectric layer is disposed. A gold subwavelength antenna element 504 is disposed over the Al ₂ O ₃ dielectric layer.

The geometry of the illustrated embodiment is characterized as: the thickness of the gold mirror is 130 nm, the thickness of the ITO layer is 16 nm, the thickness of the aluminum oxide layer is 5 nm, and the spatial dimensions of the sub-wavelength antenna elements are 180 nm x 60 nm x 50 nm. Thus, the described geometry and composition of these structures establishes magnetic resonance at the electromagnetic wavelength of 1265 nm.

Figure 5c also shows how a potential difference is applied between the gold mirror and the sub-wavelength antenna element. Accordingly, an electric field is applied between the ITO-Al ₂ O ₃ interface. As will be presented in more detail below, it is believed that the electric field can cause a change in carrier concentration at the ITO-Al ₂ O ₃ interface and, in turn, enhance the electromagnetic response properties in a desired manner. In other words, it is judged that the electric field induces the development of 'active ITO regions' with different charge carrier concentrations, shown in Fig. 5c, which locally enhance the electromagnetic response characteristics. However, the embodiments of the invention are not limited to the actual realization of this phenomenon. It has been experimentally confirmed that the electromagnetic response characteristics of the metasurface thus described, configured for near-infrared electromagnetic waves, can be tuned using an electric field.

A specific example of a metasurface reflectarray is shown in FIGS. 5A-5C and described above, but embodiments of the invention are not limited to this specifically described structure. As will be appreciated, this structure can be modified in any of a variety of ways suitable for the desired application of the metasurface. For example, although a metasurface reflectarray includes rows of subwavelength antenna elements held at the same potential, in many embodiments a localized electric field may be applied to the individual subwavelength elements, thus , can be used to more precisely modify the electromagnetic response characteristics of the metasurface. For example, in many embodiments, the metasurface is independently addressable by each of the plurality of sub-wavelength antenna elements, eg, using control circuitry commonly used in pixelated displays. Such a structure can enable broad and robust control over the localized electromagnetic response properties of the metasurface. In this way, the metasurface can be used to perform wavefront shaping in any manner suitable for the requirements of specific applications including, but not limited to, steerable optical beamforming, and holography. Of course, an electric field may be locally applied to the metasurface using any of a variety of techniques in accordance with embodiments of the invention.

In the case where a conventional power source is used to build a potential difference causing an electric field, power is only consumed greatly when the electric field change is desired, and relatively little power is used for maintaining the electric field. Thus, the described electrically tunable metasurface can be made relatively energy efficient.

Additionally, as will be appreciated, while subwavelength antenna elements having specific dimensions and geometries have been discussed above, it will be apparent that any of a variety of antenna geometries may be implemented in accordance with embodiments of the invention. In some embodiments, V-shaped antenna elements are implemented. In many embodiments, a split ring resonator is implemented. In various embodiments, the rod is implemented as an antenna element. As will be appreciated, in particular the implemented antenna elements may be based on the desired electromagnetic response characteristics of the metasurface.

Moreover, although specific hierarchical structures are discussed, any suitable structure capable of implementing a metasurface comprising a conductor-dielectric interface that provides a tunable refractive index based on an applied electric field may be implemented in accordance with various embodiments of the invention. It is also clear that For example, FIG. 6 illustrates a cross-sectional portion of a sub-gated electrically tunable metasurface in accordance with one embodiment of the invention. The metasurface is similar to that shown in Figures 5a-5c, except that the antenna is embedded in an Al ₂ O ₃ layer and an ITO layer. In particular, the metasurface reflectarray features an underlying gold mirror, on which an ITO layer is disposed, on which an aluminum oxide - Al ₂ O ₃ - dielectric layer is disposed. An ITO layer is disposed over the Al ₂ O ₃ layer, covering the sub-wavelength antenna element. In the illustrated embodiment, the thickness of the Al ₂ O ₃ layer is 10 nm, the thickness of the ITO layer is 15 nm, and the gold subwavelength antenna element thickness is 50 nm. Additionally, the planar dimensions of the gold subwavelength antenna element are 60 nm x 90 nm. It should also be noted that the potential difference is applied in the opposite manner compared to the conventional potential difference application. Of course, as before, certain dimensions are referenced, but it will be apparent that any of a variety of antenna geometries suitable for realization of a desired electromagnetic response may be implemented in accordance with embodiments of the invention. More generally, any of a variety of hierarchical structures may be implemented.

The operating kinetics of the electrically tunable metasurface thus described will now be discussed below.

Actuation of an electrically tunable metasurface configured to respond to near-optical frequency electromagnetic waves

The dynamics of metasurface tunability described above is understood as follows. When an electric field is applied between the described electrically tunable metasurfaces, it is believed that the carrier concentration at the conductor-dielectric interface will increase, forming an accumulation layer. Consequently, a complex permittivity change appears, which in turn is related to the phase and amplitude change of the reflected light.

For example, with respect to the metasurface reflectarray described above with reference to Figs. 5a-5c, to parameterize the ITO permittivity using the Drude model, the carrier concentration in the cumulative layer of ITO was 2x10 ²⁰ cm When varying between ^-3 and 1x10 ²² cm ^-3 , the real part of the permittivity of the active layer of ITO may cross over to zero in the wavelength range between approximately 0.5 μm and 3 μm. When approaching the epsilon-near-zero (ENZ) condition, a significant electric field enhancement in the cumulative layer of ITO is observed, which is easily understood from the boundary condition giving continuity of electrical displacement at the interface of two materials with different permittivity. can be Thus, the coupling of the gap plasmon resonance of the metasurface and the ENZ resonance of ITO results in a resonant frequency split that can be used for phase and amplitude modulation. This can be confirmed by calculating the phase shift and reflection coefficient of the plane wave reflected from the metasurface. Assuming that the carrier concentration of bulk ITO is 1×10 ¹⁹ cm ⁻³ and 1×10 ²¹ cm ⁻³ in the accumulation layer of ITO when the voltage is turned on, a resonant frequency split can be observed. Figure 7a shows that when the voltage is off, the magnetic resonance of the metasurface changes from 1000 nm to 1600 nm for subwavelength antenna elements configured in length from 140 nm to 220 nm. When the voltage is turned on, the plasmonic magnetic resonance couples with the ENZ region of the active ITO layer, splitting the magnetic resonance into two resonances. Figure 7b shows this resonant separation. In particular, the wavelength region where the real part ε _r of the permittivity varies from -1 to 1 is emphasized. At wavelengths at which ENZ conditions approach the cumulative layer of ITO, an improvement in the z-component E _z of the electric field in the active ITO layer can be observed. When ε _r is greater than zero, E z in the cumulative layer of ITO is parallel to E _z in _the aluminum oxide and background ITO. When ε _r is less than zero in the accumulation layer, the z-component becomes antiparallel to the E _z of the surrounding medium. FIG. 7c shows the phase shift that occurs when the charge carrier concentration in the active region of ITO changes from 1×10 ¹⁹ cm ⁻³ to 1×10 ²¹ cm ⁻³ . In particular, the dark region 702 corresponds to a 180 degree phase shift that overlaps with a -180 degree phase shift, and arrow 704 indicates a change in the amount of the phase shift. For example, starting from the bottom of arrow 704 and moving in the direction of the arrow, the phase shift is from 0 degrees to 180 degrees at the point where it reaches the dark region 702 , which is equivalent to a -180 degree phase shift . Continuing in the direction of the upward arrow 704 from the dark region 702, the phase shift is from -180 degrees to 0 degrees.

8A-8B show how reflectance and phase shift change as a function of wavelength and charge carrier concentration. In particular, FIG. 8a plots reflectance as a function of carrier concentration and wavelength. In particular, Figure 8b plots the phase shift as a function of carrier concentration and wavelength. As before, dark region 802 corresponds to a 180 degree phase shift that overlaps with a -180 degree phase shift, and arrow 804 indicates the change in the amount of phase shift. For example, starting from the bottom of arrow 804 and moving in the direction of the arrow, the phase shift is from 0 degrees to 180 degrees at the point where it reaches the dark region 702, which is equivalent to a -180 degree phase shift . Continuing in the direction of the upward arrow 804 from the dark region 802 , the phase shift is from -180 degrees to 0 degrees.

Figures 9a and 9b show how the reflection efficiency and phase can be varied as a function of carrier concentration for the metasurface shown in Figures 5a-5c. In particular, FIG. 9a shows the reflection efficiency as a function of carrier concentration in the active region of the ITO layer. In general, the reflection efficiency is relatively independent of the charge carrier concentration. 9B plots the phase shift as a function of carrier concentration. As will be appreciated, carrier concentration modifications can be used to substantially implement any desired phase shift. Although certain data are presented for certain parameters, embodiments of the invention are not limited to metasurfaces having properties corresponding to those presented in the data. Data may likewise be obtained for various electrically tunable metasurfaces in accordance with embodiments of the invention.

According to the present understanding, based on these dynamics, the operation of the described electrically tunable metasurface is made. However, as previously suggested, embodiments of the invention are not limited to the actual occurrence of the kinetics described. The scope of application encompasses the structure being described, irrespective of the actual dynamics of its operation.

approximately 10㎛ Fabrication of an electrically tunable metasurface configured to control the propagation of electromagnetic waves having a wavelength of less than

The electrically tunable metasurface described above can be fabricated in a variety of ways. For example, in many cases standard e-beam lithography techniques may be used. For example, the metasurface shown in FIGS. 5A-5C can be fabricated using the following process: A 3 nm thick Ni film can be deposited as an adhesive layer by thermal evaporation on a quartz glass substrate, and then heat A gold mirror with a thickness of 130 nm can be deposited using vapor deposition, an ITO layer with a thickness of 16 nm can be deposited using sputtering technology, an Al ₂ O ₃ layer with a thickness of 5 nm can be grown by atomic layer deposition, and the Then, using a 260 nm PMMA bilayer (PMMA-495K and PMMA-950K), the oxide surface was coated to prepare the deposition of a subwavelength antenna array, and a fishbone structure with an area of 25 μm x 25 μm, a gold connection, and Gold pads can be patterned using an e-beam lithography system (Leica Vistec EBPG 5000+) with 100 pA current (for structures) and 50 pA current (for connections and pads) with an acceleration voltage of 100 keV, after exposure and development, A 50 nm Au film can be deposited by e-beam deposition, after which the resist can be removed. Of course, while one fabrication technique has been described, any suitable fabrication technique for implementing the structures described above may be implemented in accordance with embodiments of the invention, and they may produce electrically tunable metasurfaces with varying compositions and varying geometries. can be used to manufacture. It should not be misunderstood that the described electrically tunable metasurface can only be fabricated using the specifically described techniques.

It is conjectured from the above discussion that the concepts mentioned above may be implemented in various arrangements according to embodiments of the invention. For example, any of a variety of subwavelength antenna element geometries may be employed, and any of a variety of materials may be used. Geometry and material selection can be based on the desired electromagnetic property response for the realized metasurface. Thus, while the invention has been described in certain specific forms, many additional modifications and variations will be apparent to those skilled in the art. Accordingly, the present invention may be practiced otherwise than as specifically described. Accordingly, the embodiments of the present invention are to be regarded as illustrative rather than restrictive aspects.

Claims (21)

An electrically tunable metasurface reflector array comprising:
mirrored surface,
conductive layer,
a dielectric layer, wherein the conductive layer and the dielectric layer are in direct contact to form a conductor-dielectric interface;
a plurality of sub-wavelength antenna elements;
a power source configured to establish a potential difference between at least one subwavelength antenna element and the mirrored surface;
the potential difference between the subwavelength antenna element and the mirrored surface applies an electric field to a corresponding area of the electrically tunable metasurface reflectarray;
each of the plurality of sub-wavelength antenna elements is independently addressable by the potential difference between the sub-wavelength antenna element and the mirrored surface using circuitry;
The electrically tunable metasurface reflectarray causes the electrically tunable metasurface reflectorarray to measurably enhance the propagation properties of the incident electromagnetic wave by an electric field applied in connection with the geometry and material composition of each of the dielectric layer, the conductive layer, and the subwavelength antenna elements. Tunable metasurface reflectarray. delete delete The method of claim 1,
An electric field applied in connection with the geometry and material composition of each of the dielectric layer, the conductive layer, and the subwavelength antenna elements causes the electrically tunable metasurface reflectarray to form at least a portion of the electromagnetic spectrum characterized by wavelengths less than 10 μm. An electrically tunable metasurface reflectarray for measurably enhancing the propagation properties of an incident electromagnetic wave contained therein. 5. The method of claim 4,
wherein at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength shorter than or equal to a wavelength corresponding to a wavelength of the near-infrared electromagnetic wave. 6. The method of claim 5,
An electrically tunable metasurface ripple, wherein when a region of an electrically tunable metasurface is exposed to an electric field, an incident reflected electromagnetic wave comprised within at least a portion of the electromagnetic spectrum exhibits a phase shift based on the magnitude of the applied electric field. Rect Array. 6. The method of claim 5,
wherein at least a portion of the electromagnetic spectrum is characterized by an electromagnetic wave having a wavelength corresponding to a wavelength of the near-infrared electromagnetic wave. 6. The method of claim 5,
wherein at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength shorter than or equal to a wavelength corresponding to a wavelength of visible light. 9. The method of claim 8,
wherein at least a portion of the electromagnetic spectrum is characterized by electromagnetic waves having a wavelength corresponding to a wavelength of visible light. 5. The method of claim 4,
wherein the conductive layer comprises one of a nitride-based material, silver, copper, gold, aluminum, an alkali metal, an alloy, a transparent conductive alloy, and graphene. 5. The method of claim 4,
wherein the conductive layer comprises indium tin oxide. 12. The method of claim 11,
wherein the dielectric layer comprises a dielectric oxide. 13. The method of claim 12,
wherein the dielectric layer comprises aluminum oxide. 14. The method of claim 13,
the mirrored surface comprises gold;
and at least one of the plurality of subwavelength antenna elements comprises gold. 15. The method of claim 14,
When a region of an electrically tunable metasurface reflectorarray is exposed to an electric field, the charge carrier concentration at the conductor-dielectric interface within the region is altered based on the magnitude of the applied electric field, whereby the alteration results in at least a portion of the electromagnetic spectrum An electrically tunable metasurface reflectarray in which a phase shift of a reflected incident electromagnetic wave appears within a portion. 16. The method of claim 15,
an electrically tunable metasurface reflectarray, wherein a change in charge carrier concentration from 1x10 ¹⁹ cm ^-3 to 1x10 ²¹ cm ^-3 is sufficient to shift the phase of an incident reflected electromagnetic wave that is within at least a portion of the electromagnetic spectrum by at least 2π. . 5. The method of claim 4,
and at least one of the plurality of subwavelength antenna elements conforms to a rod-shaped geometry. 5. The method of claim 4,
wherein at least one of the plurality of subwavelength antenna elements conforms to a V-shaped geometry. 5. The method of claim 4,
and at least one of the plurality of subwavelength antenna elements conforms to a split ring geometry. 5. The method of claim 4,
wherein at least two of the plurality of subwavelength antenna elements are coupled to a same conducting element coupled to the power source. 21. The method of claim 20,
An electrically tunable metasurface reflectarray, wherein rows of subwavelength antenna elements are coupled to respective conductive elements coupled to a power source.

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